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Reply to “Comment on ‘Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect' ”

R. Y. Chiao, Harold Hart, Michael Scheibner, Jay E. Sharping, Nader A. Inan, Douglas Singleton, Michael Edmund Tobar

Physical Review A, 2025

Abstract

We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.

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